论文标题
评估Krylov复杂性的饱和度作为混乱的量度
Assessing the saturation of Krylov complexity as a measure of chaos
论文作者
论文摘要
Krylov的复杂性是一种研究操作员如何在特定基础上传播的新方法。最近，已经指出该数量具有长期饱和度，取决于系统中混乱的量。由于此数量不仅取决于哈密顿量，而且还取决于所选的操作员，因此在这项工作中，我们通过研究在扩展不同操作员时的整合性与混乱过渡的整合性如何变化来研究该假设的一般性水平。为此，我们与具有横向纵向磁场的Ising链一起工作，并将Krylov复杂性的饱和度与量子混乱的标准光谱度量进行比较。我们的数值结果表明，该数量作为混沌性的预测指标的有用性在很大程度上取决于所选的操作员。
Krylov complexity is a novel approach to study how an operator spreads over a specific basis. Recently, it has been stated that this quantity has a long-time saturation that depends on the amount of chaos in the system. Since this quantity not only depends on the Hamiltonian but also on the chosen operator, in this work we study the level of generality of this hypothesis by studying how the saturation value varies in the integrability to chaos transition when different operators are expanded. To do this, we work with an Ising chain with a transverse-longitudinal magnetic field and compare the saturation of the Krylov complexity with the standard spectral measure of quantum chaos. Our numerical results show that the usefulness of this quantity as a predictor of the chaoticity is strongly dependent on the chosen operator.
